The Eurodollar futures contract expiring in December $2023$ is quoted at $98\mathrm{.}40$ and a company plans to invest $$8$ million for the three months starting in December $2023.$

a$)$ What interest rate can the company lock in using futures contracts?

b$)$ How many contracts should the company purchase to eliminate the uncertain in their investment?

c$)$ If the actual $3-$month Libor rate turns out to be $1\mathrm{.}3\%($APR$)$ in December $2023,$ describle the cash flows from the futures and the cash investment.